Are anomalous cosmic rays the main contribution to the low-energy galactic cosmic ray spectrum?

L105

The Astrophysical Journal, 680: L105–L108, 2008 June 20 

䉷 2008. The American Astronomical Society. All rights reserved. Printed in U.S.A.

ARE ANOMALOUS COSMIC RAYS THE MAIN CONTRIBUTION TO THE LOW-ENERGY GALACTIC COSMIC RAY SPECTRUM?

K. Scherer,1 _{H. Fichtner,}1_{S. E. S. Ferreira,}2_{I. Bu¨ sching,}2 _{and M. S. Potgieter}2

Received 2007 October 31; accepted 2008 May 9; published 2008 June 2

ABSTRACT

While the high-energy part of the Galactic cosmic ray spectrum is well observed, its nature at energies below about 1 GeV nucleon-1 _{is still not known well. Recent in situ measurements made with the Voyager 1 spacecraft}

in the heliosheath between the solar wind termination shock and the heliopause have added further constraints on the local interstellar spectrum of Galactic cosmic rays at low energies. We show here that they also suggest how the low-energy proton part is formed locally in the heliosphere and globally in the Galaxy. The measured flux of anomalous cosmic rays in the heliosheath is unexpectedly high compared to expectations before Voyager 1 reached the shock, which might be a temporal effect or due to an additional acceleration beyond the termination shock. Combining this finding with recent model results for astrospheres immersed in different interstellar en-vironments shows that the astrospheric anomalous cosmic ray fluxes of solar-type stars can be a hundred times higher than thought earlier and, consequently, their total contribution to the lower end of the interstellar spectrum can be significant.

Subject headings: acceleration of particles — cosmic rays — Galaxy: general — hydrodynamics — shock waves Online material: color figures

1.INTRODUCTION

Galactic cosmic rays (GCRs) of energies above 1 GeV are most probably mainly produced by the supernovae in the Gal-axy (Aharonian et al. 2004). After their initial acceleration at supernova shock waves these high-energy particles propagate diffusively through the turbulent interstellar medium (ISM). Consequently, the cosmic-ray (CR) spectrum observed at Earth is a time average over millions of years during which numerous supernova explosions inject CRs with individual acceleration spectra that are subsequently superposed and modulated due to the transport through the ISM (Bu¨sching & Potgieter 2008). While the resulting local interstellar spectra (LIS) at energies above about 10 GeV can be observed at Earth, at lower energies the additional modulation in the heliosphere makes such a direct observation impossible. Therefore, below 1 GeV the LIS are essentially unknown, except for estimates on the basis of Ga-lactic propagation models (Ptuskin et al. 2005). The study of their modulated spectra as observed with the Voyager space-craft in the heliosphere allows one, however, to constrain the probable range of differential fluxes below 1 GeV.

After the determination of the most likely (ranges of the) LIS, one can check on their origin. Flare star contributions and turbulent interstellar transport have been proposed to generate the low-energy part of the CR proton spectrum (see Schlickeiser 2002). Another scenario involves the acceleration of particles at termination shocks of OB/Wolf-Rayet stars (Casse & Paul 1980; Voelk & Forman 1982; Binns et al. 2005). In this case a contribution to the proton LIS above 1 GeV is discussed, but the acceleration in the far smaller astrospheres of solar-type stars is not addressed (Voelk & Forman 1982).

Here we argue, motivated by recent data from the Voyager 1 spacecraft (Stone et al. 2005), that the anomalous cosmic rays

1_{Institut fu¨r Theoretische Physik, Lehrstuhl IV: Weltraum- und Astrophysik,}

Ruhr-Universita¨t Bochum, D-44780 Bochum, Germany; kls@tp4.rub.de, hf@tp4.rub.de.

2_{Unit for Space Physics, North-West University, 2520 Potchefstroom, South}

Africa; stefan.ferreira@nwu.ac.za, fskib@puk.ac.za, marius.potgieter@nwu .ac.za.

(ACRs) that are accelerated at the solar wind termination shock and possibly in the heliosheath, and likewise at the termination shocks and in the astrosheaths of other solar-type stars, rep-resent a significant if not dominant contribution to the low-energy end of the Galactic proton spectrum below 1 GeV.

2.ASTROSPHERES OF SOLAR-TYPE STARS

Astrospheres of G stars (Frisch 1993), of which the helios-phere is the best example, are formed by the interaction of an outflowing stellar wind and (in the stars’ rest frame) the in-flowing interstellar matter (see Fig. 1).

The surface separating such flows is called an astropause (heliopause), at which they are in pressure equilibrium. The mutual adaptation of a supersonic stellar wind and an inter-stellar flow usually implies a inter-stellar wind termination shock inside and a bow shock outside an astrosphere. The region between the inner shock front and the astropause is called the (inner) astrosheath. The heliospheric pendant, the heliosheath, is presently being explored in situ by the Voyager 1 and 2 spacecraft which crossed the solar wind termination shock on 2004 December 16 (Stone et al. 2005) and on 2007 August 30 (Stone 2007). Recent data and modeling imply that the decade-old paradigm explaining the origin of ACRs (Potgieter 1995; Fichtner 2001) is correct although some modifications appear to be required.

So far, it has been assumed that a fraction of the interstellar neutral atoms that penetrate the heliosphere (due to its relative motion with respect to the local ISM) becomes ionized inside the termination shock. These new ions are picked up by the magnetized solar wind and are transported outward toward the termination shock, where they are diffusively accelerated to the observed energies of up to 1 GeV. Contrary to expectations,

Voyager 1 has found that the shock acceleration is neither

taking place everywhere on the shock surface nor is limited to it, because the flux of anomalous protons continues to increase well into the heliosheath (Stone et al. 2005). There is possibly additional significant (stochastic and adiabatic) acceleration in the heliosheath that was not anticipated because only recent

L106 SCHERER ET AL. Vol. 680

Fig. 1.—Computed (axisymmetric) helio/astrosphere visualized in the rest frame of the corresponding star with the color-coded proton number density. The interstellar flow is from the right. The white lines indicate the stellar wind termination shock (TS), the helio/astropause (HP/AP), and the bow shock (BS). The black line indicates the trajectory of Voyager 1 in the heliosphere. [See

the electronic edition of the Journal for a color version of this figure.]

TABLE 1 Model Values Model np (cm⫺3) nH (cm⫺3) vLISM (km s⫺1) TLISM (K) TS (AU) HP (AU) BS (AU) Heliosphere . . . 0.1 0.1 25 8000 80 120 221 Astrosphere . . . 0.04 0.24 15 3000 120 200 285 Notes.—Shown are values for the interstellar proton ( ) and hydrogennp (nH) number density, and the relative inflow speed (vLISM) and temperature (TLISM) of the local interstellar medium. The last three columns give the re-sulting helio/astrocentric distances of the termination shock (TS), the helio/ astropause (HP/AP), and the bow shock (BS) in the upwind direction.

models solve the modulation problem for a realistic large-scale heliospheric structure resulting from multidimensional (M)HD modeling (for example, Zank 1999; Mu¨ller et al. 2006; Po-gorelov et al. 2006). With such improved modeling it is straight-forward to show the potential significance of adiabatic heating and, possibly, stochastic acceleration in the heliosheath (Fer-reira et al. 2007) to explain the Voyager 1 observations. Ac-cording to this paradigm that should apply to other stars as well, the CR spectra depend not only on the individual stellar winds but also on the state of the surrounding ISM.

So far, all relevant helio/astrospheric models we are aware of discuss the CR propagation into astrospheres but not their leakage into the ISM (Frisch 2006). Here we demonstrate that the entirety of astrospheres and their different surrounding ISM, via the supply of neutral atoms into the astrosphere, are capable of producing the low-energy part of the LIS of protons below 1 GeV.

3.QUANTITATIVE MODELING

To numerically compute the interactions of astrospheres with the ISM we solve the following set of equations for mass, momentum, and energy:

⭸ ri⫹ ⵱ · (r u ) p Q ,i i p,i (1) ⭸t ⭸ (r u )i i ⫹ ⵱ · (r u u ⫹ PI) p Q ,i i i i m,i (2) ⭸t ⭸ ri_u2_⫹ Pi _{⫹ ⵱ ·} ri_{u u}2 _⫹ g u Pi i i pQ , (3) i i i e,i

(

)

(

)

which describe the balance of mass, momentum, and energy of the protons both in a stellar wind and the ISM (i p p) as well as an interstellar neutral H population (i p H). The latter is partially ionized mainly by charge exchange with solar wind protons, thus forming the pickup ion (i p PUI) for which only

the continuity equation (1) is explicitly taken into account. A fraction of these PUIs is transformed to ACRs with energies up to a few hundred MeV by the processes of shock acceleration and adiabatic heating (for the heliospheres and possibly more for astrospheres). The fluid quantities are the mass densityri, velocity ui, and pressure P Ii; and gi denote the unity tensor and the polytropic indices of the components, respectively. The time is t andQj,i denote the sources related to the interaction between various species. For a full description see Fahr et al. (2000) and Scherer & Ferreira (2005). The ACR and GCR differential intensities_{j p P f}2 are computed from their trans-port equation (Parker 1965):

df 1 ⭸f

p⵱ · (K · ⵱f ⫺ u f ) ⫹ (⵱ · u )p p ⫹ Q , (4)PUI

dt 3 ⭸ ln P

with the time t, the rigidity P, and any sourceQPUIof ACRs inside the heliosphere, the diffusion tensor K, and the omni-directional distribution function f. This equation includes all the transport processes relevant for CRs: diffusion, convection, drifts, and adiabatic energy changes.

Regarding the outer boundary conditions, one knows from astronomical observations that there exists a wide range of interstellar parameters for the number density (10⫺4 to 104

cm ) and temperature (101

–106

K), and relative speeds of 0–

⫺3

103 _{km s}⫺1 _{(Cox 2005; Tielens 2005). Also the composition}

of the ISM varies and affects, e.g., the ionization fraction. Not all combinations can occur, but there are typical parameter sets describing various stable phases of the ISM such as hot, warm, and cold states (Cox 2005; Tielens 2005; Frisch & Slavin 2006). We consider here two of the four cases analyzed in detail by Scherer et al. (2008); see Table 1. The first corresponds to the heliosphere, the second to different but not extreme conditions of the ISM around a star.

For the inner boundary at 1 AU we assume in both cases a G-type star with a proton number densityn p 5 cm⫺3, a stellar wind speed_{u p 400} km s⫺1, and a temperature_{T p 10}5 K.

4.ACR PROPAGATION INTO THE ISM

Using the data of the model described above and in detail in Scherer et al. (2008) we derived the spectra shown in Figure 2 displaying the anomalous proton spectrum (lower dash-dotted

line) at the heliopause compared to the local Galactic proton

spectrum (dotted line) in the energy range from 5 to approx-imately 50 MeV. The sum of Galactic and anomalous cosmic rays is given by the solid line, where above 50 MeV the Galactic cosmic ray spectrum dominates. The lower dashed line rep-resents the heliospheric anomalous cosmic ray spectrum at the termination shock, where the triangles are Voyager 1 mea-surements (Stone et al. 2005). The upper dashed and

dash-No. 2, 2008 ACRs AS LOW-ENERGY COMPONENT OF LIS L107

Fig. 2.—ACR spectrum at the heliopause (lower dash-dotted line) and an astropause (upper dash-dotted line). The dotted line is the interstellar proton spectrum given by Langner & Potgieter (2004) while the solid line is the combined spectrum at the heliopause including the ACRs. The dashed lines are the spectra at the termination shocks, e.g., the lower one for that of the heliosphere and the upper one for that of the astrosphere. The triangles are taken from the Voyager measurements, when crossing the termination shock (Stone et al. 2005). [See the electronic edition of the Journal for a color

version of this figure.]

Fig. 3.—Model spectra and Voyager 1 data in the heliosheath. The helio-pause (HP) is at 130 AU. The dashed lines describe, from bottom to top, the proton LIS at 5, 10, 15, and 20 MeV. The solid lines are the corresponding ACR fluxes. The triangles and diamonds are the 18–27 MeV and 4–6 MeV proton data as observed. Beyond the heliopause the flux decreases with a profile. [See the electronic edition of the Journal for a color version of

2

1/r

this figure.]

dotted lines give the corresponding spectra for an astrosphere, described in Table 1, for the termination shock and astropause, respectively. Figure 3 shows the radial intensity increase in the heliosheath superposed with the Voyager 1 data.

Obviously, the anomalous protons represent the dominant contribution to the LIS of protons below 25 MeV for the he-liosphere and below a 100 MeV for the selected astrosphere. Higher values are to be expected for more extreme states of the ISM as discussed by Mu¨ller et al. (2006) and by Scherer et al. (2006). These astrospherically induced LIS will be mod-ified by interstellar propagation effects. In particular, the low-energy particles can undergo stochastic acceleration and, there-fore, can easily contribute in astrospheres to the flux up to 1 GeV.

In order to estimate the total contribution by all astrospheres in the Milky Way to the interstellar CR energy density, one has to integrate the spectra with respect to energy and the resulting flux per steradian over a star centered source surface. Subsequently, one has to take into account the residence time of CRs in the Milky Way and the number of relevant stars. Following the outlined procedure, the spectra in Figure 2 are divided into the two energy intervals as indicated in the figure, i.e., from 5 to 300 MeV (interval 1) and above 300 MeV (interval 2).

For the heliospheric ACRs, we integrate the ACR spectrum in region 1 at the heliopause, leading to a flux of ,

6 ⫺2 ⫺1

FACR(helio) p 4p j(ACR) E dE p 1.2 # 10 MeV m

∫

.

6 ⫺2 ⫺1

FACR(astro) p 9.2 # 10 MeV m s

Now approximating an astropause (of a solar-type star in an LISM-like environment) by a sphere with radiusR p 200AU (see Table 1) an integration over its surface yields the total

energy output _{Q p 0.5 F}

_∫

where the factor 0.5 accounts approximately for the fact that an astropause cannot be considered as a surface with a ho-mogeneous source distribution of ACRs.

The CR energy spectrum at any given location in the Milky Way is obtained from the superposition of all individual source spectra, in particular those provided by astrospheres. A quasi– steady state is established by the fact that the CRs injected by stars into the ISM are not accumulating there unlimitedly but escape after a typical residence time of _{t ≈ 2 # 10}7 yr (De

e

Marco et al. 2007; Strong et al. 2007). It follows from the above estimates that a solar-type star injects an energy of eV into the Milky Way during this period.

55

Eastrop3.2 # 10

The Milky Way contains about_{4 # 10}11stars of which 6.5% are G stars (K. Strassmeier 2007, private communication). Be-cause also the stars with the neighboring spectral types, i.e., F (3%) and K (13%), drive similar winds, we include those in our estimate. This 22.5% of the stellar population corresponds to approximately_{0.9 # 10}11stars in the Milky Way. Therefore we find a total injected energy related to ACRs of about eV. To obtain their average energy density in the

66

2.8 # 10

Milky Way we assume a disk radius and height of its diffusive volume to be 15 and 2 kpc, respectively, resulting in eV cm . Using the heliospheric

val-⫺2 ⫺3

eastro(ACR)≈ 7.6 # 10

ues, one obtainsehelio(ACR) p 3.2 # 10⫺3eV cm , which we⫺3 consider as a lower limit.

Computing the GCR energy density from the corresponding spectrum (dashed lines in Fig. 2) we finde_totp1.0eV cm⫺3 in accordance with the values given in the literature; e.g., Web-ber (1998) or Schlickeiser (2002). Below 300 MeV the energy density is 13% of this value. Therefore, the energy density provided by solar-type stars in that energy interval (!_{300 MeV)} can amount to about 50% of the observed value and is obvi-ously a significant contribution. One should be aware that the energy density resulting from the heliospheric flux is only 2.5% of that in the ISM for energies below 300 MeV, but it is unlikely that all solar type stars are surrounded by the same local in-terstellar environment. Furthermore, keeping in mind that in this estimate all other spectral types are neglected, the contri-bution from all astrospheres should be expected to be much higher than 50%. Therefore, all CR fluxes in region 1 shown in Figure 2 can be interpreted as of anomalous (as opposed to

L108 SCHERER ET AL. Vol. 680 supernova-induced) origin. The fluxes produced by a given star

are merging within a few hundred AU with the background flux, which is the superposition of the corresponding fluxes of all other ACR-producing stars in the Milky Way.

5.CONCLUSION

Despite further complications, such as different ISM, more violent stellar winds, or interstellar transport, we have dem-onstrated that the ISM is able to produce, via astrospheric PUI production, its own low-energy CR proton spectrum (!₃₀₀ MeV) via acceleration in astrosheaths and that a contribution of supernova-accelerated CRs to this low-energy part of the interstellar spectrum may not be required, although—most likely—is present.

Also, the explanation for an LIS with heavier CRs below 1 GeV might require a stellar wind contribution. It has been argued that for heavier CRs there is a possibility of distin-guishing the direct stellar (anomalous) contribution to the LIS from that of supernova-accelerated GCRs, namely the isotopic composition, which is different for ACRs and GCRs

(Cum-mings & Stone 2007) as prominently evidenced by the22_Ne/ 20

Ne ratio. This high ratio can, however, only be explained with the assumption of a significant contribution by the winds of Wolf-Rayet stars (Casse & Paul 1982; Prantzos et al. 1987; Binns et al. 2005). So, even in this case an (possibly indirect but) important CR component (see also Binns et al. 2007; Lingenfelter & Higdon 2007) is eventually resulting from the astrospheres of (non-solar-type) stars.

So far, of course, our knowledge results from modulated CR spectra. Only future measurements with either the Voyagers, when they reach the local ISM, or with missions such as the proposed Interstellar Heliopause Probe (ESA) or the

Inter-stellar Probe (NASA), which will penetrate the heliopause to

explore the region beyond, will be able to clarify the true (local) interstellar cosmic ray fluxes.

H. F. and K. S. are grateful to the Deutsche Forschungs-gemeinschaft for funding the Heliocauses project. I. B., S. E. S. F., and M. S. P. acknowledge the partial financial support of the SA National Research Foundation and the SA Centre for High Performance Computing.

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